MinT - Best Known (211−60, 211, s)-Nets in Base 3

Best Known (211−60, 211, s)-Nets in Base 3

(211−60, 211, 282)-Net over F₃ — Constructive and digital

Digital (151, 211, 282)-net over F₃, using

3¹ times duplication [i] based on digital (150, 210, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 70, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(211−60, 211, 554)-Net over F₃ — Digital

Digital (151, 211, 554)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−60, 211, 13632)-Net in Base 3 — Upper bound on s

There is no (151, 211, 13633)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47110 714226 878119 956919 399122 150278 565947 570984 165682 738931 209006 655378 043293 619052 088652 439631 706425 > 3²¹¹ [i]